Abstract : Many problems of signal processing, beam forming, and image transmission require the rapid generation of linear transforms of a spatial or temporal signal. The most commonly required transforms are the Fourier transform, the discrete Fourier transform, and the Hadamard transform. Other frequently used transforms include the Laplace transform, the Z-transform, and the Mellin transform. The purpose of the apparatus of this invention is to rapidly perform such linear transforms with small lightweight special-purpose hardware.